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Old January 1, 2009, 05:27 AM   #1
Ftom14cat
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doubling shotgun = 4x recoil energy?

According to Understanding Firearms Ballistics by Robert Rinker, a shotgun that truly doubles (both barrels fire at exact same time) would have not twice the recoil energy, but quadruple. Is this true, and if so why?

The weight and velocity of the charge etc remain the same, but the gun comes back with twice the velocity, thus quadruple the energy.
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Old January 1, 2009, 05:58 AM   #2
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double double

I had a SXS double on me once when a turkey popped up literally from underneath my feet. It was an interesting feeling. I missed the bird. The gun hasn't done it since.
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Old January 1, 2009, 08:22 AM   #3
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The recoil engery of a gun is the recoil energy of the bullet divided by the ratio of the bullet's mass to the gun's mass.
If the gun weighs 100 times more than the bullet, the gun will have 1/100 the energy of the bullet. If the gun weighs 50 times more than the bullet, the gun will have 1/50 the energy of the bullet. This does not include the gunpowder gasses which also contribute to recoil.

This is how energy divides up, the momentum of the gun is always equal to the momentum of the bullet.

When you shoot both barrels at once, you not only double the bullet energy, you also double the bullet weight so the recoil doubles twice.

If instead of doubling a double barrel, you had shot two single barrel shotguns at the same time, then the bullet weight and gun weight both would be double and you would experience double the recoil energy.
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Old January 1, 2009, 08:29 AM   #4
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I built a set of line array, open baffle cabinet speakers several years ago. I use a one watt amplifier to drive 16 full range speakers. It easily outclasses my 100 watt home stereo with better sound at a much higher volume since power curve is exponential. Energy is funny that way.
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Old January 1, 2009, 09:33 AM   #5
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A .22 cal varmint rifle shooting a 52 grain bullet at about 3900 fps and a .45-70 shooting a 405 grain bullet 1400 fps have nearly identical bullet energys but the .45-70 kicks way harder than a .22 varmint rifle.

Also, compare a .44 magnum recoil when fired from a 3 pound revolver to the recoil of that same bullet shot from a 7 pound rifle.
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Old January 1, 2009, 01:06 PM   #6
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When something you expect to be doubled is quadrupled, it's typically the result of something being squared. For example, if you buy 100 feet of rope and double it, you'll have 200 feet. If you buy a 10-foot square tarp, you'll have 100 sq ft of tarp. If you double the 10 foot dimension to a 20-foot square tarp, you'll have 400 sq ft of tarp. Without seeing Robert Rinker's calculations, or test results, it's hard to verify his assertion.

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Old January 1, 2009, 02:08 PM   #7
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Thanks for the help yall
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Old January 1, 2009, 09:33 PM   #8
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Energy (recoil)= mass*(velocity)^2 ---> Energy (recoil)= 2mass*(2velocity)^2
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Old January 1, 2009, 09:48 PM   #9
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The beretta 682 gold e has done exactly this to me. What you say about quadrupling the recoil isnt true but it at least doubles it . I was shooting double trap at the West Virginia state shoot and I accidently forgot to check the barrel select and it was selected for the top chamber. The gun doubled and I got knocked over practically and the first target was completely gone, the only bad thing was that the recoil broke one of the firing pins. So yes the doubling of a shotgun is at least two times the dramage so 3 1/4 is 6 1/2 or even more.
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Old January 1, 2009, 11:52 PM   #10
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Calculating a shotgun’s recoil: (Smokeless Powder).

(((SW + WW) * MV) + (4700 * PW)) ^ 2 / (GW * 64.348) = RE

Where:
SW = Weight of shot, in pounds
WW = Weight of wad, in pounds
PW = Weight of powder, in pounds
GW = Weight of gun, in pounds
MV = Muzzle velocity, in feet per second
RE = Recoil energy, in foot pounds

Assuming both barrels are loaded with the same load, if they fire simultaneously, the Recoil Energy will be quadrupled. In actual practice, the simultaneous discharge of both barrels is pretty much impossible. If one is 3 or 4 milliseconds behind the other, the RE is actually two jolts of the same energy, so doubled would be more like reality.

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Old January 2, 2009, 03:20 AM   #11
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My A.H. Fox 16 ga. doubled on me once!!!! I knew it instantly!!!!!! I can't recall exactly why it did it but I took it to my gunsmith and he diagnosed it and fixed it. I think one of the triggers had a worn sear and it slipped?????

Not something I look forward to experiencing again. I figure that's probably what a .416 rigby feels like. I guess it's good to know I could shoot one if I had to!!!!!
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Old January 2, 2009, 09:05 AM   #12
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I am not sure on the details, but I am sure that B.L.E. was correct as far as the 'it is because you double the weight of the projectile without doubling the weight of the gun.' I believe the actual recoil is only 2x, but the felt recoil is much more. I think you are applying the same acceleration from twice the mass to the same mass so you get double the acceleration.
F=MA
Mass of bullet X Accelleration of Bullet = Mass of Gun X acceleration of Gun
2Mass of Bullet X Acceleration of Bullet = Mass of Gun X 2 acceleration of Gun


But I did get C in Physics.
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Old January 2, 2009, 09:28 AM   #13
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The recoil is only doubled, not quadrupled.

Edit: After thinking about it, the recoil would be quadrupled. I was only thinking of the kinetic energy of the two loads firing simultaneously. The kinetic energy of the combined load is twice that of the single load, but the recoil of the shotgun itself is quadrupled.
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Old January 2, 2009, 10:30 AM   #14
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243:

You have bad math. The second equation is incorrect.
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Old January 2, 2009, 12:41 PM   #15
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Are we talking about momentum or energy?

The momentum of the gun is always equal and opposite to the momentum of the bullet, regardless of the gun's mass.

Since two loads of shot have twice the mass of one shot, they together have twice the momentum and thus the equal and opposite momentum of the gun must be doubled as well.

Momentum = mass X velocity

Since the mass of the gun is fixed, in order to double its momentum, you must double its velocity.

Kinetic energy = mass X velocity^2 / 2

When you double the velocity of a mass, you quadruple its kinetic energy.

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Old January 2, 2009, 01:14 PM   #16
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B.L.E.

look at 243's right side equation. It is wrong, your equation is correct.

243's right equation doubles the velocity, which is incorrect.

2m*((v^2)/2) does not equal 2M*(2V^2)
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Old January 2, 2009, 03:12 PM   #17
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Recoil Formula from Hodgdon reloading manual :


ReCoil Energy (in Ft Lbs) =

(Bw Mv + 4700 Pw) ^ 2
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64.348 X Gw


Bw Weight of Wad and shot in lbs (convert shot weight to grains then add the weight of the wad in grains and divide sum by 7000 = lbs )
Mv Muzzle velocity of load in fps ( from loading tables )
Pw Weight of powder in load - in lbs ( number of grains / 7000 )
Gw Gun Weight - used catalog specs from Browning


7000 Grains / Lb
437.5 Grains / Ounce

Shot WT Ounces Grains by Gague
1 1/8 oz = 1.125 oz 492 12 ga
1 oz = 1.0 oz 438 12 ga
7/8 oz = .875 oz 383 20 ga
3/4 oz = .750 oz 328 28 ga
1/2 oz = .500 oz 219 .410 ga

12 gauge Wad, 1 oz, typically is 33 grains
WAA12 12 ga wad is 39 gr
WAA20 20 ga wad is 30.8 gr

Recoil calculation using a Browning O/U XS Skeet model 12ga:

1 1/8 oz 18 gr clays 1200 FPS
492gr 18gr 1200 fps
XS skeet 30" barrels 7.9375 lbs Bw 0.075 lbs
Pw 0.003 lbs
Recoil 20.40 Ft Lbs Base Line

If you double the shot load ( so both barrels go off at once to 984 grains / and the 18 grains of powder to 36 grains ) you have to leave the velocity the same - because both shells develop 1200 fps - the forumula above will give you 77.16 Ft Lbs of Recoil or about 3.78 times the recoil vs one shell going off.
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Old January 2, 2009, 03:42 PM   #18
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Many of you are confusing or failing to distinguish between momentum and energy.

The recoil momentum of the gun is doubled because the mass of the projectile is doubled. Since the gun's mass doesn't change, its recoil velocity must double to conserve momentum. This means that the recoil energy of the gun is quadrupled. Rinker is correct.
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Old January 2, 2009, 09:25 PM   #19
.45 COLT
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Quote:
the forumula above will give you 77.16 Ft Lbs of Recoil
I believe you forgot to add a second wad.

DC
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Old January 2, 2009, 10:12 PM   #20
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Seen laughing at the thought.
I would say the energy of multiple barrels would compound the felt recoil because:
Both barrels are not going to go off at an identical time and the slight recoil of the first shell would be similar to just one shot out of a lighter shotgun.
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Old January 5, 2009, 01:12 PM   #21
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.45 Colt - you are correct / thanks for catching my error.

My original calculation did not double the weight of the wad. When I did the math again (this time including the weight of the 2nd wad as well ) / the recoil from both barrels going off at the same time is 4.000 times the original recoil. 81.62 Ft Lbs vs the original 20.40 Ft Lbs.
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Old January 5, 2009, 03:15 PM   #22
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I'm old enough to have taken my university engineering pre hand-held calculator. With a slide rule, one could lose track of the decimal point's position -- it was common for the numbers to be correct, but off by several factors of 10. Consequently, designs based on those calcs could be off by factors of ten, also.

One of the most valuable things I learned was from an old Heidelberg Don... A student's concrete column had an unbelievable amount of reinforcing steel, and the student said his numbers supported the design. The professor replied, "I don't care how accurate your numbers are, is your solution reasonable?"

You need to ask yourself, does quadrupling the recoil when a shotgun doubles seem reasonable? Initially, it didn't to me, yet I've run the numbers several times using different approaches. Like BigJimP's numbers, mine support the 4 X times increase. Numbers aside, it's DaveBeal's simple explanation that seems to clarify the physics.
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Old January 5, 2009, 03:47 PM   #23
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I agree Zippy .... Slide Rules and Fortran IV punch cards ..... now those were the days ....before hand held calculators were even invented...
I'm old enough to have done it the old way too....and an Excel Spreadsheet is sure a big time upgrade over those days.....

but since I blew the calculation .... your point is well taken as a reminder that using it still depends on the ability to reason your way thru the problem, checking the forumlas, and checking and verifying the results ( which I didn't do )... ( and making sure the results I saw were reasonable ) which I didn't do obviously...

Doing it quick / and blindly regurgitating the numbers - is no shortcut for doing it correctly. But this was an interesting thread - because initially, I didn't think it was 4 Times ....and it led me astray. I may have napped during some of those physics classes in the early 70's .....
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Old January 5, 2009, 08:15 PM   #24
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Quote:
You need to ask yourself, does quadrupling the recoil when a shotgun doubles seem reasonable?
Felt recoil is a much more complicated topic than total recoil, because it depends on how suddenly the recoil occurs, and because it involves human perception. I don't know whether felt recoil is more closely related to recoil momentum or recoil energy, but I agree that the quadrupling of recoil energy, while true, is counterintuitive.

Quote:
Numbers aside, it's DaveBeal's simple explanation that seems to clarify the physics.
Glad you like it!

Last edited by DaveBeal; January 5, 2009 at 09:17 PM.
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